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TAX PROGRESSION UNDER COLLECTIVE WAGE BARGAINING AND INDIVIDUAL EFFORT
DETERMINATION
ERKKI KOSKELA RONNIE SCHÖB
CESIFO WORKING PAPER NO. 2024
CATEGORY 4: LABOUR MARKETS JUNE 2007
Presented at CESifo Area Conference on Employment and Social Protection, May 2007
An electronic version of the paper may be downloaded • from the SSRN website: www.SSRN.com • from the RePEc website: www.RePEc.org
• from the CESifo website: Twww.CESifo-group.deT
CESifo Working Paper No. 2024
TAX PROGRESSION UNDER COLLECTIVE WAGE BARGAINING AND INDIVIDUAL EFFORT
DETERMINATION
Abstract We study the impact of tax policy on wage negotiations, workers’ effort, employment, output and welfare when workers’ effort is only imperfectly observable. We show that the different wage-setting motives – rent sharing and effort incentives – reinforce the effects of partial tax policy measures but not necessarily those of more fundamental tax reforms. Although a higher degree of tax progression always leads to wage moderation, the well-established result from the wage bargaining literature that a revenue-neutral increase in the degree of tax progression is good for employment does not carry over to the case with wage negotiations and imperfectly observable effort. While it remains true that introducing tax progression increases employment and output, we cannot rule out negative effects from an increase in tax progression when tax progression is already very high. Welfare effects are ambiguous a priori but we derive sufficient conditions for welfare improving revenue-neutral increases in tax progression.
JEL Code: J41, J51, H22.
Keywords: wage bargaining, effort determination, tax progression.
Erkki Koskela Department of Economics
P.O. Box 17 Arkadiankatu 7
00014 University of Helsinki Finland
Ronnie Schöb School of Business & Economics
Free University Berlin Boltzmannstr. 20
14195 Berlin Germany
June 2007 This paper has been part of the CESifo project “How to construct Europe”. Koskela thanks Otto-von-Guericke-University Magdeburg for great hospitality as well as the Research Unit of Economic Structures and Growth at the University of Helsinki, the Yrjö Jahnsson Foundation and the Academy of Finland (grant No. 1117698) for financial support. Schöb thanks the WZB in Berlin for great hospitality. The authors are grateful for comments by Lazlo Goerke, Thomas Moutos and from seminar participants at the WZB, Göteborg University, Nordic Tax workshop in Bergen and CESifo area conference on Employment and Social Protection. The usual disclaimer applies.
1
1. Introduction
The result that tax progression leads to wage moderation and is good for employment has
been derived for different assumptions about the wage-setting motives such as rent sharing in
wage bargaining models (see, e.g., Holm and Koskela 1996, Koskela and Vilmunen 1996,
Koskela and Schöb 1999). The results for efficiency wage models, where firms unilaterally
decide upon both the wage rate and the employment level, are, however, still mixed. Wage
moderation has a positive effect on labour demand but a negative effect on individual labour
effort and thus workers’ productivity. Hoel (1990) was the first to analyze the overall effect of
tax progression in such a framework by showing that a higher marginal income tax rate,
which leaves the average tax level unchanged at the initial equilibrium wage rate, will
decrease the gross wage and unemployment (see also Goerke 1999) but Fuest and Huber
(1998) show that, for a rise in tax progression such that the tax burden per worker is the same
in the old and new equilibrium, the result might be reversed.1
It is important to emphasize that the effect of tax progression, however, has not yet been
analyzed in a uniform framework that combines these different wage-setting motives. So far,
only very few papers have combined wage bargaining and effort considerations at all. Early
contributions by Lindbeck and Snower (1991) and Sanfey (1993) do not provide a uniform
answer to the question as to how far different wage-setting motives analyzed in efficiency
wage and union bargaining models reinforce or weaken each other. Later, Bulkley and Myles
(1996) show that with imperfect monitoring of workers’ effort, monopoly trade unions will
set a higher wage than the pure efficiency wage set by the firms. This provides a higher bonus
for non-shirking and results in a higher level of effort than we would observe in a competitive
labor market. Garino and Martin (2000), on the other hand, show that efficiency wages offset
1 All these results do not carry over to models where workers differ in their productivity or when we allow for
market entry. A tax reform that raises marginal tax rates at all income levels and increases (decreases) average taxes at high (low) income levels may lead to higher gross wages and unemployment (see Andersen and Rasmussen 1999). With free entry and exit of firms, Rasmussen (2002) shows that in the long run, changes in profits may imply that higher wage tax progressivity will negatively affect employment if the marginal tax rate is too high.
2
the cost of higher wages and induce firms to make more concessions in wage negotiations.
Thus there is theoretical evidence that the different wage-setting motives reinforce each other.
Within such a framework, Altenburg and Straub (1998) analyze variations of the benefit-
replacement ratio. They find that, in contrast to the standard result in both efficiency wage and
union bargaining models, the effect of a higher reservation utility on wages, employment, and
effort is ambiguous when benefits are financed through lump-sum taxes. A higher
replacement ratio may then reduce the wage rate and raise employment. A higher reservation
utility of workers will induce firms to reduce their demand for effective labor. If, as a
consequence, the labor share decreases, firms experience a higher relative reduction in profits
from a wage increase. This explains why the wage may actually fall and – in the end –
employment will rise.
To our knowledge, only Garcia and Rios (2004) analyze the impact of taxes in this
framework. They adopt the Altenburg and Straub (2002) model to analyze revenue-neutral tax
reforms only numerically. Their numerical calculations suggest that a revenue-neutral
increase in the tax exemption that is financed by an increase in the wage tax increases
employment. This indicates that the result by Koskela and Schöb (1999), according to which a
revenue-neutral shift from payroll taxes to wage taxes raises employment when there is a
higher tax exemption for the latter, also applies when effort is unobservable. Furthermore,
they argue that it is better for employment in the case of constant fiscal revenues to
compensate higher tax exemption through increases in wage taxes rather than payroll taxes.
Since Garcia and Rios (2004) only provide numerical, rather than analytical, results, we first
present an analytical framework to elaborate the way in which tax policy affects wage
negotiations and employment when effort is only imperfectly observable and trade unions and
firms negotiate on wages and then study the impact of a revenue-neutral increase in tax
progression on wage formation, effort determination and employment.
Our comparative statics analysis indicates that the standard results from the trade union
literature must be modified in the case of imperfect monitoring of individual effort
determination. In these standard models, tax policy only affects wages by altering the size of
3
the labor surplus. When both wage-setting motives are present, however, tax policy also
affects the strength with which tax policy parameters affect the negotiated wage and
employment. When effort is not observable, tax policy affects the wage elasticity of effort,
which in turn affects the wage elasticity of labor demand. Since these elasticities alter the
scope with which workers can attract labor rents, this constitutes an additional channel by
which tax policy can influence the wage negotiation. As it turns out, this additional impact
reinforces the effects of partial tax policy measures that we observe in the standard
bargaining and efficiency models.
In the second main part of the paper, we then analyze revenue-neutral tax reforms that
change the degree of tax progression, and derive the qualitative effects such tax reforms have
on the negotiated wage, individual effort, and aggregate employment. Table 1 highlights the
importance of such an analysis. The labor tax systems in all the OECD countries are
progressive and show significant differences in the degree of tax progression. We measure tax
progression by the difference between marginal and average tax rates that are shown in the
first and second columns.2 This difference, reported in the third column, is known as the
average wage tax progression ARP (see Lambert 2001, chapters 7 and 8 and our section 5).
The higher this difference, the more progressive wage taxation is. The highest difference is
for France, with 19.2 percentage points, and the lowest one for Canada, with only 1.4
percentage points.
2 To make these figures comparable with our stylized model framework below, all tax rates are with reference
to the gross wage, including payroll taxes paid by the employer.
4
Table 1: Labor taxation in the OECD countries
(1) (2) (3) (4)
Country Average wage tax
Marginal wage tax
average wage tax rate
progressionARP
Calculated relative tax exemption
a/w Australia 28.6 35.4 6.8 22.9 Austria 44.9 55.5 10.6 56.1 Belgium 54.2 66.4 12.2 34.8 Canada 32.3 33.9 1.6 26.4 Czech Republic 43.6 48.1 4.5 34.9 Denmark 41.5 49.2 7.7 20.7 Finland 43.8 55.1 11.3 36.6 France 47.4 66.6 19.2 30.3 Germany 50.7 64.0 13.3 44.9 Greece 34.9 44.2 9.3 95.2 Hungary 45.8 54.7 8.9 52.3 Iceland 29.7 40.4 10.7 30.7 Ireland 23.8 33.2 9.4 49.5 Italy 45.7 58.0 12.3 46.7 Japan 26.6 31.5 4.9 47.8 Korea 16.6 24.8 8.2 80.0 Luxembourg 31.9 45.9 14.0 64.5 Mexico 15.4 23.4 8.0 78.1 Netherlands 43.6 50.7 7.1 56.6 New Zealand 20.7 33.0 12.3 37.3 Norway 36.9 43.2 6.3 25.4 Poland 43.1 45.7 2.6 33.7 Portugal 32.6 39.4 6.8 60.0 Slovak Republic 42.0 48.3 6.3 52.1 Spain 38.0 45.5 7.5 43.3 Sweden 48.0 51.7 3.7 17.0 Switzerland 28.8 36.5 7.7 46.7 Turkey 42.7 44.5 1.8 12.5 United Kingdom 31.2 40.6 9.4 35.1 United States 29.6 34.1 4.5 22.5
Source: OECD (2004) Legend: Tax rates are for the year 2004 for a single person with 100% of average wage, relative to the gross wage including the social security contributions paid by employees. Column (3) shows the difference between marginal and average rate of income tax. As an approximation it is assumed that for each country the tax schedule consists of a tax exemption and a constant marginal tax rate. The exchange rate between US dollar and euro was assumed to be unity. Social assistance level does not include housing costs. Numbers for social assistance are from 2002 and taken from OECD (2004), Benefits and Wages, OECD Indicators.
Our first main result shows that an increase in wage tax progression always leads to wage
moderation. In this respect, our model shows that the wage moderation effect of higher tax
progression that is present in both the efficiency wage model and the bargaining model carries
over to the more general case when both wage-setting motives are at work. The effect of
higher tax-revenue neutral progression on effort and, consequently, on labor demand,
however, is a priori ambiguous. Although it remains true that introducing tax progression
raises employment, it turns out that the claim “tax progression is good for employment”
(Koskela and Vilmunen 1996) only applies to moderate degrees of tax progression.
5
In section 2 below, we present the basic structure of the model and describe the time
sequence of decisions with respect to wage bargaining, labor demand, and individual effort
determination. The workers’ individual effort determination and the firms’ labor demand are
elaborated in section 3. Section 4 uses the Nash bargaining approach to analyze wage
negotiations subject to firms’ labor demand and workers’ effort determination and presents
the essential comparative static results. Section 5 applies the analysis to revenue-neutral
changes in the labor tax structure and explores the effects of tax progression on the negotiated
wage, individual effort, and employment. The main findings are summarized in section 6.
2. Basic framework Concerning the time sequence of decisions, we assume that the government behaves as a
Stackelberg leader who fixes the tax parameters in the first stage. To raise revenues, the
government can employ a wage tax t, which is levied on the gross wage w minus a tax
exemption a . Thus the tax base for the wage tax t equals Law )( − , where L denotes total
employment. In the presence of a positive tax exemption a, the marginal tax rate t exceeds the
average tax rate )1( watt a −≡ so that we have a linearly progressive tax system, with
progression depending positively on the wage rate. The net-of-tax wage workers receive is
given by tawtwn +−= )1( . We abstract away from payroll taxes.
At stage 2, firms and trade unions bargain with respect to the gross wage.3 They take the
tax parameters as given and anticipate the consequences that the negotiated gross wage has
for labor demand by firms and also that the resulting net labor income has for individual effort
determination by workers. After the wage negotiations are settled, at stage 3 the firms decide
about their labor demand. Since firms cannot perfectly observe effort, the firms have to
anticipate the workers’ individual effort decisions. At the final stage, stage 4, workers make
their individual effort choice. The time sequence of decisions is summarized in Figure 1. In
3 Since tax parameters are given from the viewpoint of firms and trade unions, it does not matter whether they
bargain over gross or net-of-tax wages (see Koskela and Schöb 2002).
6
the subsequent sections we derive the decisions taking place at different stages by using
backward induction.
Figure 1: Time sequence of decisions
1 s tag es t
Ta x policy( , )t a
W ag eba rga ining ( )w
La bo rde m an d ( )L
Effo rtde te rm in ation ( )e
2 s ta gen d 3 sta gerd 4 s taget h
3. Individual effort determination and labor demand We start by analyzing the 4th stage, where workers decide about their working effort, taking
the tax policy, the negotiated wage, and aggregate employment as given. Then we analyze
stage 3, where firms determine employment.
3.1. Individual effort determination
We focus on the choice that a single worker faces when employed by a representative firm in
a static framework. Since effort cannot be fully controlled by firms, they can set a standard
effort that we normalize to one. If workers meet this standard, their jobs are secure. If they
shirk by providing less effort, however, firms can fire them. The employment probability can
thus be described by a minimum function. For effort lower than the standard we assume, for
analytical convenience, an iso-elastic probability function of employment de where 0>d
denotes the (constant) employment probability elasticity of effort.4 The employment
probability rises with effort for 1<e and is 1 for higher effort level so that we have the
employment probability function ),1min( de≡ρ and the probability of being laid off is
),1min(1 de− . The parameter d is increasing in both monitoring intensity and monitoring
4 We exclude the case where d = 0 because in this case, the job would be secure even without providing effort
and total output would fall to zero. This would lead firms to set a wage rate equal to zero. Both employment supply and demand would then be indetermined. Futhermore, note that if the detection probability should be concave in effort, we would have to assume 1≤d .
7
efficiency. Low values of d makes it less risky for workers to shirk while +∞→d implies
perfect monitoring and the firing of all workers who do not meet the working effort standard.
Imperfect monitoring implies that when assuming a representative risk-neutral worker
and applying a specific utility function V that is additively separable and quasi-linear, we
obtain
(1) ( )beegweV dndw ),1min(1)]()[,1min( −+−= ,
where b denotes the workers’ outside option, which equals some exogenous unemployment
income, and )(eg denotes the disutility of effort e as a convex function, i.e.
0)('',0)(' >> egeg .5 Working time per worker is assumed to be fixed and normalized to
unity.
For the following, it is convenient to define the workers’ surplus as the difference
begws n −−≡ )( . This allows us to rewrite the utility function as bseV dw += , which splits
the utility into the expected surplus when working with effort e and the basic income b ,
which the household receives in any case. The optimal individual effort level can be derived
from the first-order condition 0)('1 =−= − egesdeV ddwe . The worker chooses an effort level at
which the expected utility loss of working harder, which occurs with probability de , equals
the expected utility gain from an increased probability of staying in employment and
receiving the surplus s. Using the parameterization 1,/)( >θθ= θeeg , the effort function
becomes:
(2) ( ) ( )θθθθ
−≡−⎟⎠⎞
⎜⎝⎛
θ+θ
=111
1
bwAbwd
de nn .
It is straightforward to show that individual effort is increasing in the net-of-tax wage rate,
and decreasing in the outside option. This implies that we have 0<te , because this lowers the
net-of-tax wage and thus reduces the penalty when caught shirking. Accordingly, we observe
5 In what follows, the derivatives of functions with one variable will be denoted by using primes, while partial
derivatives will be denoted by subscripts indicating what variable we are differentiating with respect to.
8
0>we and 0>ae . In fact, we have at et
awe )( −−= , a property we will employ later on. The
wage elasticity of effort is
(3) 0)(
)1(>
−θ−
=≡εbwtw
ewe
nw .
The respective partial derivatives with respect to the outside option b, the tax exemption a,
and the tax rate t are
(4) 0)()1(
2 <−θ−
−=εbw
ttwna ,
(5) 0)()(2
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
<=>
−θ−
=εbwabw
nt as 0⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
<=>
− ab .
The partial derivatives (4) and (5) depend on the effects the respective parameters have on the
net-of-tax wage relative to the income surplus of working. With respect to an increase in the
tax rate, this effect is ambiguous since a rise in the wage tax lowers )1( tw − but at the same
time raises the effective tax credit ta . A higher tax rate always increases the difference
between the net-of-tax rate in absolute terms, but it may lower the relative difference, which is
decisive for the elasticity if the tax exemption a is very generous. If ab = , the wage elasticity
of effort is unaffected by t since in this case we have ))(1()( bwtbwn −−=− . A higher tax
exemption a implies that a wage rate increase has a lower relative impact on the net-of-tax
wage and thus implies a lower wage elasticity of effort. Only if ab > , a rise in the tax rate
increases the impact a rise in the wage rate has on effort: the higher t is, the stronger the
relative increase of bwn − due to a wage increase is and thus the stronger the relative effect
on individual effort.
The direct effect of a change in the tax exemption is unambiguous. An increase in the tax
exemption implies that a marginal wage increase now has a lower relative impact.
9
3.2. Labor demand
In the 3rd stage of the game, each firm takes the tax parameters and the negotiated wage as
given and decides about the labor demand L by taking into account how the representative
worker will adjust effort. To derive an explicit solution, we postulate a decreasing returns-to-
scale Cobb-Douglas production function in terms of labor and effort:
(6) δ−δ
−δδ
=1
)(1
)( eLeLf , 1>δ .
Profit is given by wLeLf −=π )( . Since firms anticipate the effort level, workers will provide
( 0=eV ), and the first order profit maximization condition is weeLfL −==π )('0 . Using this
specification, we obtain the following labor demand function:
(7) 1−δδ−= ewL .
The partial derivative of labor demand with respect to the tax parameters and the negotiated
wage rate are as follows: 0)1( 1 <−δ= −eeLL tt , 0)1( 1 >−δ= −eeLL aa ,
0))1(()1( 121)1( <δ+δ−ε−=−δ+δ−= −−δδ−−δ−δ− wLeewewL ww .Since the wage tax and the tax
exemption are levied on workers, they only affect labor demand via the workers’ individual
effort, which depends on the net-of-tax wage rate. The wage rate w affects labor demand in
two different ways. Note that the standard assumption that profit decreases with increases in
the wage rate implies that the wage elasticity of effort is smaller than one, i.e. 1<ε . For the
concave production function (6), the wage elasticity of labor demand depends on both the
technological parameter δ and the wage elasticity of individual effort ε as defined in (3):
(8) δ+δ−ε=δ≡− )1(*
LwLw .
The wage elasticity of labor demand is lower compared to the case where wages do not affect
effort. It now depends negatively on the wage elasticity of effort. For 10 <ε≤ we have
δ≤δ< *1 . Hence, in the presence of unobservable individual effort determination the wage
elasticity of labor demand depends on the tax structure and thus tax policy levied on workers.
10
If, for instance, a tax reform increases the wage elasticity of effort, labor demand would
become less elastic. A wage rise would then be less costly for a trade union since the firm
would then lay off fewer workers.
The firm’s indirect profit function, which we will use in the next section, can be obtained
by inserting labor demand (7) into the profit function wLeLf −=π )( :
(9) )1(
)(),(11
11*
−δ=−=π
−δδ−−δδ−δδ− ewewewfew .
Having analyzed workers’ and firms’ behavior with respect to effort and labor demand, we
can now turn to the collective wage bargaining of stage 2.
4. Collective wage bargaining
To derive the negotiated wage, we apply the Nash bargaining solution within a ‘right-to-
manage’ model according to which employment is unilaterally determined by the firms. The
wage bargaining takes place in anticipation of the optimal employment decision by the firms
and the optimal individual effort decision by workers (2).6
The trade union maximizes the sum of the workers utility wV , and the utility of the
unemployed. Since those caught shirking and fired are replaced by unemployed workers, the
expected utility of an unemployed worker is (for inner solutions with 1<ρ ):
(10) ))(()1()1(1 *egwLN
LebLN
LeV nddu −−
−+⎟⎠⎞
⎜⎝⎛
−−−= .
While we assume that a single worker who is caught shirking will become and remain
unemployed as well as receive b , from the viewpoint of the trade union, an unemployed
member will replace a laid-off worker with the lay-off probability, which is de−1 times the
6 Bulkley and Myles (1997) have analyzed the generalized Nash bargain between a trade union and a firm
over employment level and effort level and showed that higher union power will lead to a reduction in the agreed effort level. But they do not study the impact of labor taxes on employment and effort levels.
11
employment share. We can rewrite the linear utilitarian objective function of the trade union
as
(11) NbLesLNVLVU uw +=−+= ** )()(ˆ ,
where the first term captures the workers’ surplus from employment and the second term
captures the exogenously given minimum income for all N members. *L denotes optimal
employment and *e optimal effort in the s term. We denote the relative bargaining power of
the union by β , and that of the firm by )1( β− , and assume that the threat points of the trade
union and the firm are described by NbU =0 and 00 =π , respectively. Applying the Nash
bargaining solution, the negotiating parties decide on the wage w in order to solve
(12) {β−βπ=Ω
1*
)(
)( UwMaxw
, s.t. 0=π= LeV ,
where **0 )(ˆ LesUUU =−= is the bargaining surplus to the trade union by including the
disutility of effort and *π is the indirect profit, presented in equation (9). The Nash bargaining
solution satisfies the following first-order condition:
(13) 0)1( *
*
=ππ
β−+β=Ω www U
U .
As shown in appendix A, we can solve the first-order condition (13) to find the following
implicit Nash bargaining solution for the wage rate in the presence of individual effort
determination:
(14) ⎥⎦⎤
⎢⎣⎡
−−
≡⎥⎦⎤
⎢⎣⎡
−−
⎟⎟⎠
⎞⎜⎜⎝
⎛ε−−δε−−δ+β
=ttabM
ttabw
11)1)(1()1)(1( ,
where 1>M for 1<ε . The negotiated gross wage rate depends on the exogenous income b
when unemployed, the wage tax t and the tax exemption a . Furthermore, it also depends on
the mark-up M that, apart from exogenous parameters, also depends on the wage elasticity of
effort ε .
12
Before we analyze comparative statics of the general case (14), we will first briefly
discuss several special cases, which can be analyzed within the framework we have developed
here.
A. Observable effort
When effort is observable and verifiable, it can become part of the wage contract. If the
contract specifies some fixed effort level e , we obtain the standard right-to-manage model of
union bargaining, where the wage depends on the bargaining power of the trade union and the
(constant) wage elasticity of labor demand in the case of a Cobb-Douglas production function.
Since a constant individual effort e implies 0=ε and a zero probability of being caught
shirking, i.e. 1=ρ , we have
(15a) ⎥⎦⎤
⎢⎣⎡
−−+
≡⎥⎦⎤
⎢⎣⎡
−−+
⎟⎟⎠
⎞⎜⎜⎝
⎛−δ−δ+β
==ρ=ε
ttabegM
ttabegw
1)(
1)(
)1()1(
10 ,
which implies a surplus of =s ( )tabeg −+⎟⎟⎠
⎞⎜⎜⎝
⎛−δβ )(
)1(. From (15a), we can easily derive the
special cases of a monopoly union
⎥⎦⎤
⎢⎣⎡
−−+
⎟⎠⎞
⎜⎝⎛
−δδ
==β=ρ
=εt
tabegw1)(
110
and the competitive labor market outcome where unions have no bargaining power and the
gross wage only compensates for the disutility of working
⎥⎦⎤
⎢⎣⎡
−−+
==ρ
=β=εt
tabegw1)(
10 ,
in which case the firm exploits the complete workers’ surplus, i.e. 0=s .
Alternatively we can consider the case where worker can determine their effort
unilaterally but the firm can observe the effort level. It could then pay a wage per unit of
effective labor input eL. This requires a modification of (1) such that
)()1( egtaetwV w −+−= . Since the tax exemption does not affect the wage rate anymore, in
this case the optimal effort is [ ] 11
* )1( −θ−= twe and the effort elasticity 0)1/(1 >−θ=ε is
13
constant. The profit function becomes weLeLf −=π )( with the firm maximizing with
respect to eL . This gives the following wage elasticity of labor demand
ε+δ=δ≡− */ LwLw . The negotiated wage per worker then becomes7
(15b)
( )
[ ] ( )⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
−−
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
−θ⎥⎦
⎤⎢⎣
⎡−θβ
−βε+−δ
θε+β+−δ=
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
−−+
⎟⎟⎠
⎞⎜⎜⎝
⎛βε+−δ
ε+β+−δ=
θ−θ
θ−θ
θ−θ
θ−θ
=ρ≠ε
)1(.
)1()1(
)1(
)1()1(
)1()(
)1()1()1(
1
1
1*
1
10
ttab
ttabegw
The results are similar to the results by Hansen (1999, his case 2) who develops a model
where workers can unilaterally determine their hours of work and where workers and firms
then negotiate upon the hourly wage. The structure of the solution (15b) is qualitatively
similar to that of (15a) in the sense that in both cases the mark-up is independent of tax
instruments.
B. Unobservable effort without bargaining
When 0=β , the firm unilaterally sets the wage. From the first-order condition 0* =πw , it
follows immediately that the firm acts according to the well-known Solow-condition (Solow
1979), i.e. we have 1=ε and thus
(16) ⎥⎦⎤
⎢⎣⎡
−−
≡⎥⎦⎤
⎢⎣⎡
−−
⎟⎠⎞
⎜⎝⎛
−θθ
==π t
tabMttabw
w 111 0.
The model therefore also captures the essence of the efficiency models with a (constant)
mark-up over the outside option.
C. Unobservable effort with bargaining: comparative statics
For the general case, we have 0)1( >ε− and the mark-up is larger than one when the trade
union has some bargaining power, i.e. 0>β . It increases with the relative bargaining power
7 A proof is available from the authors upon request.
14
of the trade union β , and depends negatively on the direct wage elasticity of labor demand δ .
The wage rate now depends, in addition to the relative bargaining power, the wage elasticity
of labor demand, the exogenous income, and the tax parameters, on the elasticity of effort
determination ε . Furthermore, unlike in the case of observable effort, the exogenous income
b when unemployed, the wage tax rate t , and the tax exemption a will also affect the wage
rate via the mark-up M .
The impact of a better monitoring of workers on the negotiated wage is zero as the wage
elasticity of effort is not affected by monitoring. We can thus focus on the comparative statics
of the tax parameters and the outside option in what follows.
The derivative of the mark-up with respect to ε is 0)1()1( 21 >ε−−δβ= −−εM . The mark-
up with respect to effort e is 0=eM . Since condition (14) is an implicit function of w , we
can derive the partial derivative with respect to, for example, a by taking the total derivative
( ) ( ) dattM
ttabM
ttabMdw aw ⎥
⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛−−
+⎟⎠⎞
⎜⎝⎛
−−
ε=⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
−−
ε− εε 1111 .
By rearranging, we obtain
(17) {{
011
1<⎟
⎠⎞
⎜⎝⎛−−
Δ+⎟
⎠⎞
⎜⎝⎛
−−
⎟⎟⎠
⎞⎜⎜⎝
⎛ε
Δ=
−−
−+
ε
32143421ttM
ttabMw aa
with [ ] 0)1)((1 1 >−−ε−≡Δ −ε ttabM w . In the Nash bargaining solutions with observable effort
(15a) and (15b), the mark-up is independent of a . With unobservable effort, however,
workers will increase effort when the tax exemption rises. When workers have some
bargaining power, i.e. 0>β , this ceteris paribus lowers the mark-up because a lower wage
elasticity of effort implies a higher wage elasticity of labor demand (see equation (8)). A
higher wage then induces less effort, which makes the worker less productive. As a
consequence more layoffs result from a wage increase.
The effect of the wage tax rate can be expressed as
15
(18) {{
0)1(1
12 >⎟⎟⎠
⎞⎜⎜⎝
⎛−−
Δ+⎟
⎠⎞
⎜⎝⎛
−−
⎟⎟⎠
⎞⎜⎜⎝
⎛ε
Δ=
++
++
ε
4342143421tabM
ttabMw tt .
The total effect of a higher wage tax rate on the negotiated wage is a priori ambiguous. When
we assume ab ≥ , both the effect on the mark-up and the effect on the total outside option
with the given mark-up are unambiguously positive.
Hence, tax parameters in our model with both Nash wage bargaining and individual effort
determination affect both of these via a change in the difference between the net-of-tax wage
income and the outside option as well as via a change in the mark-up.
We summarize our new characterization of the negotiated wage under individual effort
determination in
Proposition 1: Unobservable individual effort determination strengthens the
partial effects tax policy measures have on the negotiated wage compared to the
case where effort is observable. Decreasing the tax exemption lowers the
negotiated wage, while an increase in the wage tax rate increases the negotiated
wage under a sufficient but not necessary condition ab ≥ .
We can easily verify that the effects indeed reinforce each other. If we take the partial
derivative of (15a), we obtain the comparative statics effect for the standard bargaining model
with
011
0 <⎟⎠⎞
⎜⎝⎛−−
==ρ=ε
ttMwa ,
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−
−+=
=ρ=ε 21
01)(
tabegMwt .
For (15b), we similarily find
011
0 <⎟⎠⎞
⎜⎝⎛−−
==ρ≠ε
ttMwa ,
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−−
==ρ≠ε 21
01 t
abMwt .
For ab ≥ , the effects tax parameter changes have on the negotiated wage when effort is
observable are always reinforced when effort is not observable. The partial derivative of
16
equation (16) with respect to a shows the same result for the efficiency wage model: the
different wage-setting motives thus reinforce the partial tax policy effects on gross wages. We
should note, however, that in the case where ab ≤ and 0)( >−+ abeg we would obtain
opposite partial effects for changes in the wage tax rate. An increase in the wage tax will then
increase the gross wage when effort is observable but will lower the gross wage when effort is
unobservable.8
As we pointed out when discussing (15b), the reinforcing effect is also present in a model
with endogenous effort determination.
5. The impact of a tax-revenue-neutral change in tax progression on wage formation, employment, effort, output, and welfare
We are now ready to analyze what are the impacts a revenue-neutral restructuring of the labor
tax, i.e. the degree of wage tax progression, on wage formation, individual effort
determination, and employment. The effect of wage tax progression, which keeps the tax
revenue [ ]LawtG )( −= constant, can be written in the following way:
[ ]dwLawttLtLdaLdtawdG w)()(0 −++−−== . Recalling the definition of the average tax
as ( )watt a −≡ 1 , this can be expressed as
(19) dwtttdt
tawda
a
dG
)()( *
0
δ−+
−=
=.
An appropriate and intuitive way to define tax progression is to look at the average tax rate
progression (ARP), which is given by the difference between the marginal tax rate t and the
average tax rate t a , attARP −= . The tax system is progressive if ARP is positive, and tax
progression is increased if the difference increases (at a given income level, see Lambert
8 We mentioned before that our model also allows us to capture the essence of a model where workers can
endogenously determine working hours when working hours are observable, see the discussion of equation (15b). Interpreting our model as a model of imperfectly observable effective working hours we can i) confirm the results derived by Hansen (1999) for perfectly observable working hours and ii) also find the reinforcing effect when effective working hours cannot be perfectly monitored.
17
2001, chapters 7 and 8). The term *δ− att indicates the marginal tax revenue per worker
when the gross wage increases. It can be decomposed in such a way that we have a tax
progression effect and a tax level effect: )1( *δ−+ atARP . The total effect is non-positive for
a linear tax system with 0=ARP since 0)1( * ≤δ− , but may eventually become positive if
the tax system is sufficiently progressive since the employment effect is weighted by the
average tax rate only. As we will see later on, the degree of tax progression is decisive for the
way in which a revenue-neutral change in tax progression affects both employment and
individual effort.
5.1 Revenue-neutral tax progression and the negotiated wage
The total effect of changes in the tax parameters t and a on the negotiated wage is
(20) dawdtwdw at += ,
with the partial derivatives derived in section 4. Substituting (19) into the RHS of (20) for da
gives
(21) dwtttwdtw
tawdtwdw
a
aat ⎥⎦
⎤⎢⎣
⎡ δ−+
−+=
*)( ,
and, thus, the total effect of a revenue-neutral increase in the wage tax rate is
(22) 1*0 )(1
)(
−= δ−−
−+
=tttw
wt
aww
dtdw
aa
at
dG
.
In what follows, we assume Laffer-efficiency in the sense that a higher wage tax increases tax
revenues while a higher tax exemption leads to lower tax revenues even when we take
account of the indirect effects via changes in w. With respect to the tax exemption, we then
have
01ˆ*
<⎟⎟⎠
⎞⎜⎜⎝
⎛ δ−−−=+−=
tttwtLwGtLG
a
aawa .
18
Substituting the partial derivatives aw from (17) and tw from (18) into the numerator of (22)
shows that the numerator is unambiguously positive (see appendix B). Hence, we have the
following:
Proposition 2 (wage moderation): A revenue-neutral increase in wage tax
progression will moderate the negotiated wage in the presence of individual effort
determination.
The interpretation is straightforward as it turns out that the numerator in equation (22) denotes
the compensated effect an increase in the tax rate has on the wage, keeping the value of the
Nash maximand constant (see appendix C). The revenue-neutral increase in the tax exemption
fully offsets the income effect of the higher wage tax so that only the substitution effect of this
progression-enhancing tax reform remains. This finding shows that the result from
conventional ‘right-to-manage’ models in the absence of effort considerations (see, e.g.,
Koskela and Vilmunen 1996) also applies when we allow for unobservable individual effort
determination.
5.2 Revenue-neutral tax progression and individual effort determination
The total effect of changes in the tax parameters t and a and the negotiated wage on effort
determination is dwedaedtede wat ++= . Substituting the RHS of the tax-revenue neutrality
(19) for da and using aw et
te )1( −= gives
(23)
( )
{( ) .)1(
1)(
0
*
0
*
00
43421
4342144 344 21
−
=+
−
==
=
δ−+−=
⎟⎠⎞
⎜⎝⎛ δ−++
−+=
dG
aa
dGa
awat
dG
dtdwttt
te
dtdwett
tee
tawe
dtde
The direct effects of tax progression parameters on effort will cancel out so that it is only the
induced wage-moderation that affects individual effort decisions. The term tea measures the
19
impact one additional euro has on individual effort. A wage reduction of one euro reduces the
net-of-tax wage by )1( t− so that effort falls by ttea )1( − . But wage-moderation also affects
the amount by which the tax exemption can be raised. It will be lower than the neutral effect
of raising a by taw )( − if 0* <δ− att . This always holds in a linear tax system because in
this case .0)1( * <δ−t But if the tax system becomes very progressive, so that given the
marginal tax rate t the average tax rate ( )watt a −≡ 1 becomes lower and thereby 01 * >δ− at
might be the case, individual effort eventually will fall. This case is also the more likely, the
smaller the wage elasticity of labor demand and the average tax burden are. If we assume a
labor share of 2/3, we have 3=δ , and an average tax below 1/3 would suffice to let effort fall
when tax progression rises. Formally, we have
(24) *
0
10 δ⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
>=<
⇔⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
<=>
=
a
dG
tdtde .
A sufficient, but not a necessary, condition for individual effort to fall is 1<δt since we have
δ<δ* and tta < . These findings can be summarized in
Proposition 3 (individual effort determination): A revenue-neutral increase in
wage tax progression will decrease (increase) individual effort if (i) the wage
elasticity of labor demand and/or (ii) the marginal tax rate are sufficiently low
(high). A sufficient condition is 1<δt ( 1>δt ).
5.3 Revenue-neutral tax progression and employment
Finally, we consider the employment effect. The total effect of changes in the tax parameters t
and a and the negotiated wage on employment is dwLdaLdtLdL wat ++= . Substituting the
RHS of the tax-revenue neutrality for da and using ** )(at e
tawe −
= , wLLw
*** δ
−= and
*
** )1(
eeL a
a−δ
= gives
20
(25)
( )
( )0
****
**
0
***
0
***
*
0
)1(
1))(()1(
=
==
=
⎥⎦
⎤⎢⎣
⎡−−
−=
⎟⎠⎞
⎜⎝⎛ −++
−+
−=
dGa
a
dGa
awat
dG
dtdw
wLett
teL
dtdwLtt
tLe
tawe
eL
dtdL
δδδ
δδ
44 344 21
The first two terms cancel out since they cover the change in t and a that ceteris paribus
would leave the average tax burden, and thus the net-of-tax wage, constant. Hence, we are left
with two effects. As we have seen in section 5.2, the tax reform affects individual effort
depending on the wage elasticity of labor demand and the size of tax parameters. If – as is
likely - effort decreases, labor productivity falls and ceteris paribus employment. On the other
hand, the wage-moderating effect increases labor demand for any given effort level. The total
effect thus becomes ambiguous. From proposition 3 we can immediately infer
Proposition 4 (rising employment): A sufficient, but not necessary, condition
that a revenue-neutral increase in wage tax progression will increase employment
is tt a ≥δ* .
From proposition 4 follows immediately that starting from a linear tax system with tt a = ,
employment will definitely rise. This leads to
Corollary 1 (rising employment): Introducing tax progression is good for
employment when wages are negotiated and effort is determined individually.
Although we have seen that different wage-setting motives reinforce tax policy effects on
gross wages, this is not no longer true with respect to employment. With observable and
verifiable effort, employment is always increasing when tax progression rises. When effort is
unobservable and not verifiable, we find a countervailing effect via the adverse effect a rise in
tax progression has on individual effort.
21
5.4 Revenue-neutral tax progression and output
Effort and employment may go in opposite directions so that the output effect is a priori
ambiguous. Substituting equation (7) in equation (6) shows that output is proportional to wL .
The total effect of a revenue-neutral tax reform is then given by
[ ]LdwwdLeLdf +−δδ= −1)1()( . Substituting in equation (25) thus yields for a revenue-
neutral rise in tax progression
(26) 0
***
*
0
1)()1(1
)(==
⎥⎦
⎤⎢⎣
⎡−+−
−−
=dG
aa
dG dtdwtt
teewL
dteLdf δδδ
δδ .
If tt a ≥δ* , i.e. 1)1( 1* ≥−δ −aw , output is increasing. This can be summarized in
Proposition 5 (rising output): A sufficient, but not necessary, condition that a
revenue-neutral increase in wage tax progression will increase employment is
tt a ≥δ* .
Proposition 5 implies that starting from a linear tax system with tt a = , output will also rise
when tax progression is introduced so that we have
Corollary 2 (rising output): Introducing tax progression raises output when
wages are negotiated and effort is determined individually.
5.5 Revenue-neutral tax progression and welfare
Finally we want to briefly discuss the welfare implications. An appropriate measure of
welfare in our framework is the sum of profits and workers’ surplus, i.e.
(27) [ ]
[ ] [ ] bNLegbwLbNLegbeLf
GLNbLegtatwwLeLfW
++−−δδ
=++−=
+−+−+−+−=
)(1
)()(
)()()1()(
where wLeweLeLf 1111)1(
1 )1()1()()1()( −−δδ−−δ−δ
− −δδ=−δδ=−δδ= . In general the welfare
effects are affected in different directions by the parameters that specify the production
22
technology and the disutilty from effort so that general unambiguous statements cannot be
derived. However, the properties of the model allow us to derive at least some sufficient
conditions for welfare to improve.
First, note that the worker’s surplus s is increasing in effort. This follows from the
worker’s optimal effort choice, i.e. 0)('1 =−= − egesdeV ddwe , from which follows that
)(1 egds −θ= . Hence, when worker chooses a higher level of individual effort they are always
better off. Second, when employment rises those additional workers that find employment are
better since 0)( >−− begwn . Thus no worker will lose when employment is rising. Finally,
profit is increasing in output as profit is given by )()1( 11 eLfwL −− δ=−δ Hence, a sufficient
condition for a positive welfare effect is that the reform does not lead to a fall in effort,
employment and output. A necessary condition for the first requirement to hold is 1* ≥δat . A
sufficient condition for the latter two requirements is tt a ≥δ* . Thus 1* ≥δat suffices to fullfill
all three requirements. This leads to our last proposition.
Proposition 6 (rising welfare): Welfare is always increasing when a revenue-
neutral increase in wage tax progression will increase effort.
Workers only increase effort when they are better off. Since for a revenue-neutral increase in
tax progression, higher effort is always associated with higher employment and output, more
workers benefit from the higher surplus per worker and profit increases as well.
6. Conclusions
We have provided an extended framework to study the implications of the imperfectly
observable individual effort of workers on the negotiated wage and the impact of a revenue-
neutral change in the wage tax progression on wage negotiations, individual effort,
employment, output and welfare. The first, and most important, result is that a higher degree
of tax progression in this framework always leads to wage moderation. Our model confirms
this result for the case of observable effort and wage bargaining as well as for the case where
23
firms set efficiency wages unilaterally: the different wage-setting motives reinforce partial tax
policy effects present in each model. However, when effort is not observable and verifiable,
the clear-cut effect well-known from the wage bargaining literature that tax progression is
good for employment does not carry over to the case of imperfectly observable effort. In the
general case, it remains true that introducing tax progression is good for employment, but if
the adverse effect on effort becomes sufficiently large due to too high a degree of tax
progression, we cannot rule out the case where employment falls as a consequence of a
progressivity-enhancing tax reform. Since higher effort level are only observed when workers
are better off by providing more effort, increasing effort indicates that welfare is
unambiguously improving. Since in this case both profits and workers’ surplus increase,
increasing effort as a consequence of a revenue-neutral increase in tac progression is even a
sufficient condition for a strict Pareto improvement.
References
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24
Koskela, E. and R. Schöb (1999): Does the composition of wage and payroll taxes matter under Nash bargaining?, Economics Letters,64, 343-349.
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Appendix A: the negotiated wage
This appendix develops the expressions for the terms ** ππw and UUw in the first-order
condition (13) that determines the Nash bargaining solution. We start by looking at the profit
response of the firm to a change in the wage rate. The indirect profit function was presented in
equation (9). By applying the envelope theorem, according to which the effect which takes
place through the labor demand vanishes at the optimum, we find that
(A1) [ ]
[ ] ,01)(1)(
))(1())(1()1(
1
11111
121*
<ε−−=⎥⎦⎤
⎢⎣⎡ −=
−δ−−δ−δ
=π
−δδ−−−δδ−
−δδ−−δδ−
wew
ewewew
eweew
w
ww
from which it follows that
(A2) 0)1)(1(*
*
<ε−−δ
−=ππ
ww
as .1<ε With respect to the trade union’s utility, we find that
(A3) [ ]))((')1( ***
begwwegtwwLU n
ww −−δ−−−= ,
25
where *
** )1(
LwLw−=ε+ε−δ=δ . Thus, it follows that
(A4) ⎥⎥⎦
⎤
⎢⎢⎣
⎡
−−
−−δ−−−=
begwbegwwegtw
wUU
n
nww
)())((')1(1
*
**
.
Substituting (A4) and (A2) into (14) yields
(A5) [ ][ ] )1)(1)(1(
)())((')1(
*
**
ε−−δβ−=−−
−−δ−−−β
begwbegwwegtw
n
nw .
This can be rewritten as:
(A6)
[ ]
[ ][ ]
[ ][ ][ ]**
*
*
*
*
**
)1)(1)(1()(
)1)(1)(1)(1()1(')1(*)1)(1)(1())((
)1)(1)(1(')1()1)(1)(1)()((
)1)(1)(1())((')1(
βδ+ε−−δβ−−+−=
ε−−δβ−−−−δ−−−β
⇔βδ+ε−−δβ−+−=
ε−−δβ−−δ−−−β
⇔ε−−δβ−+−=
ε−−δβ−−−−δ−−−β
tabeg
twtwwegtwbeg
wwwegtwbeg
wbegwwegtw
w
nnw
nnw
.
Using the definition of the total wage elasticity of labor demand *δ , we obtain by making use
of equations (2) and (3)
(A7) [ ][ ])1)(1()()1(
')1)(1()1( * ε−−δ+β−+=⎥⎥⎦
⎤
⎢⎢⎣
⎡
−β+ε−−δ− tabeg
twwegtw w
so that
(A8) [ ][ ])1)(1()()(
)1)(1()1( * ε−−δ+β−+=⎥⎦
⎤⎢⎣
⎡+θ
β+ε−−δ− tabegd
dtw
Using the explict functional form for effort yields for the disutility of effort
[ ]btatwddeg −+−θ+= − )1()()( 1* . Substituting in (A8) yields
(A9) [ ]
( ) [ ])1)(1(1
)1)(1()(
)1)(1()1(
ε−−δ+β⎥⎦
⎤⎢⎣
⎡−⎟
⎠⎞
⎜⎝⎛
θ+−=
⎥⎦
⎤⎢⎣
⎡ε−−δ+β
θ+−
+θβ+ε−−δ−
tabd
d
dd
ddtw
26
Rearranging yields
(A10) [ ][ ])1)(1()1)(1()1( ε−−δ+β−θ+
θ=⎥⎦
⎤⎢⎣⎡
θ+θ
ε−−δ− tabdd
tw
which gives equation (14).
Appendix B: the sign of the numerator of (22)
Substituting the partial derivatives (19) and (20) into the numerator of (22) yields
(B1) .0
)1()(
)1(
1)1()()(
2
2
<−−
Δ−
−ε
Δ−=
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
−−
−−−
Δ+⎟
⎠⎞
⎜⎝⎛ ε
−+ε
Δ=
−+
ε
ε
tbwM
tM
taw
tabM
tawMw
taww
n
atat
Appendix C: the Slutzky-decomposition for the total effect of the wage tax on the negotiated wage
Differentiating the indirect Nash maximand 01** Ω=π=Ω β−βU , where *sLU = and **** )1()( LswLef +−=π , with respect to t and a gives
(C1) (i) 0)(*1*11*1* <−πβ−=πβ=Ω β−−ββ−−β awLUUU tt ,
(ii) 0*1*11*1* >πβ=πβ=Ω β−−ββ−−β tLUUU aa .
The wage tax has a negative effect and tax exemption has a positive effect on the Nash
maximand. Using the comparative statics, the indirect Nash maximand can be inverted in
terms of a for the function ),( 0Ω= tha . Substituting this for a in 01** VU =π=Ω β−β gives
the compensated indirect Nash maximand 00* )),(,( Ω=ΩΩ tht .9 Differentiating this
compensated indirect Nash maximand with respect to t gives 0** =Ω+Ω att h so that
tawh att /)(/ ** −=ΩΩ−= . This describes the relationship of tax parameters to keep the Nash
maximand constant.
9 See Diamond and Yaari (1972).
27
According to the duality theorem, the Nash maximand wage function w and the
compensated wage function cw at the same Nash maximand level are equal, so that we have
),()),(,( 00 Ω=Ω twthtw c . Differentiating this with respect to the wage tax gives ctatt wwhw =+ so that we obtain the Slutsky equation
(C2) actt w
tawww )( −
−= ,
where the total effect of the wage tax rate has been decomposed into the negative substitution
effect ( 0<ctw , see Appendix C) and the positive income effect ⎟
⎠⎞
⎜⎝⎛ −− aw
taw )( . QED.
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and Growth, April 2007 1964 Steven Brakman and Charles van Marrewijk, It’s a Big World After All, April 2007 1965 Mauro Ghinamo, Paolo M. Panteghini and Federico Revelli, FDI Determination and
Corporate Tax Competition in a Volatile World, April 2007 1966 Inés Macho-Stadler and David Pérez-Castrillo, Optimal Monitoring to Implement Clean
Technologies when Pollution is Random, April 2007 1967 Thomas Eichner and Ruediger Pethig, Efficient CO2 Emissions Control with National
Emissions Taxes and International Emissions Trading, April 2007 1968 Michela Redoano, Does Centralization Affect the Number and Size of Lobbies?, April
2007 1969 Christian Gollier, Intergenerational Risk-Sharing and Risk-Taking of a Pension Fund,
April 2007 1970 Swapan K. Bhattacharya and Biswa N. Bhattacharyay, Gains and Losses of India-China
Trade Cooperation – a Gravity Model Impact Analysis, April 2007 1971 Gerhard Illing, Financial Stability and Monetary Policy – A Framework, April 2007
1972 Rainald Borck and Matthias Wrede, Commuting Subsidies with two Transport Modes,
April 2007 1973 Frederick van der Ploeg, Prudent Budgetary Policy: Political Economy of Precautionary
Taxation, April 2007 1974 Ben J. Heijdra and Ward E. Romp, Retirement, Pensions, and Ageing, April 2007 1975 Scott Alan Carson, Health during Industrialization: Evidence from the 19th Century
Pennsylvania State Prison System, April 2007 1976 Andreas Haufler and Ian Wooton, Competition for Firms in an Oligopolistic Industry:
Do Firms or Countries Have to Pay?, April 2007 1977 Eckhard Janeba, Exports, Unemployment and the Welfare State, April 2007 1978 Gernot Doppelhofer and Melvyn Weeks, Jointness of Growth Determinants, April 2007 1979 Edith Sand and Assaf Razin, The Role of Immigration in Sustaining the Social Security
System: A Political Economy Approach, April 2007 1980 Marco Pagano and Giovanni Immordino, Optimal Regulation of Auditing, May 2007 1981 Ludger Woessmann, Fundamental Determinants of School Efficiency and Equity:
German States as a Microcosm for OECD Countries, May 2007 1982 Bas Jacobs, Real Options and Human Capital Investment, May 2007 1983 Steinar Holden and Fredrik Wulfsberg, Are Real Wages Rigid Downwards?, May 2007 1984 Cheng Hsiao, M. Hashem Pesaran and Andreas Pick, Diagnostic Tests of Cross Section
Independence for Nonlinear Panel Data Models, May 2007 1985 Luis Otávio Façanha and Marcelo Resende, Hierarchical Structure in Brazilian
Industrial Firms: An Econometric Study, May 2007 1986 Ondřej Schneider, The EU Budget Dispute – A Blessing in Disguise?, May2007 1987 Sascha O. Becker and Ludger Woessmann, Was Weber Wrong? A Human Capital
Theory of Protestant Economic History, May 2007 1988 Erkki Koskela and Rune Stenbacka, Equilibrium Unemployment with Outsourcing and
Wage Solidarity under Labour Market Imperfections, May 2007 1989 Guglielmo Maria Caporale, Juncal Cunado and Luis A. Gil-Alana, Deterministic versus
Stochastic Seasonal Fractional Integration and Structural Breaks, May 2007 1990 Cláudia Costa Storti and Paul De Grauwe, Globalization and the Price Decline of Illicit
Drugs, May 2007
1991 Thomas Eichner and Ruediger Pethig, Pricing the Ecosystem and Taxing Ecosystem
Services: A General Equilibrium Approach, May 2007 1992 Wladimir Raymond, Pierre Mohnen, Franz Palm and Sybrand Schim van der Loeff, The
Behavior of the Maximum Likelihood Estimator of Dynamic Panel Data Sample Selection Models, May 2007
1993 Fahad Khalil, Jacques Lawarrée and Sungho Yun, Bribery vs. Extortion: Allowing the
Lesser of two Evils, May 2007 1994 Thorvaldur Gylfason, The International Economics of Natural Resources and Growth,
May 2007 1995 Catherine Roux and Thomas von Ungern-Sternberg, Leniency Programs in a
Multimarket Setting: Amnesty Plus and Penalty Plus, May 2007 1996 J. Atsu Amegashie, Bazoumana Ouattara and Eric Strobl, Moral Hazard and the
Composition of Transfers: Theory with an Application to Foreign Aid, May 2007 1997 Wolfgang Buchholz and Wolfgang Peters, Equal Sacrifice and Fair Burden Sharing in a
Public Goods Economy, May 2007 1998 Robert S. Chirinko and Debdulal Mallick, The Fisher/Cobb-Douglas Paradox, Factor
Shares, and Cointegration, May 2007 1999 Petra M. Geraats, Political Pressures and Monetary Mystique, May 2007 2000 Hartmut Egger and Udo Kreickemeier, Firm Heterogeneity and the Labour Market
Effects of Trade Liberalisation, May 2007 2001 Andreas Freytag and Friedrich Schneider, Monetary Commitment, Institutional
Constraints and Inflation: Empirical Evidence for OECD Countries since the 1970s, May 2007
2002 Niclas Berggren, Henrik Jordahl and Panu Poutvaara, The Looks of a Winner: Beauty,
Gender, and Electoral Success, May 2007 2003 Tomer Blumkin, Yoram Margalioth and Efraim Sadka, Incorporating Affirmative
Action into the Welfare State, May 2007 2004 Harrie A. A. Verbon, Migrating Football Players, Transfer Fees and Migration Controls,
May 2007 2005 Helmuth Cremer, Jean-Marie Lozachmeur and Pierre Pestieau, Income Taxation of
Couples and the Tax Unit Choice, May 2007 2006 Michele Moretto and Paolo M. Panteghini, Preemption, Start-Up Decisions and the
Firms’ Capital Structure, May 2007
2007 Andreas Schäfer and Thomas M. Steger, Macroeconomic Consequences of Distributional Conflicts, May 2007
2008 Mikael Priks, Judiciaries in Corrupt Societies, June 2007 2009 Steinar Holden and Fredrik Wulfsberg, Downward Nominal Wage Rigidity in the
OECD, June 2007 2010 Emmanuel Dhyne, Catherine Fuss, Hashem Pesaran and Patrick Sevestre, Lumpy Price
Adjustments: A Microeconometric Analysis, June 2007 2011 Paul Belleflamme and Eric Toulemonde, Negative Intra-Group Externalities in Two-
Sided Markets, June 2007 2012 Carlos Alós-Ferrer, Georg Kirchsteiger and Markus Walzl, On the Evolution of Market
Institutions: The Platform Design Paradox, June 2007 2013 Axel Dreher and Martin Gassebner, Greasing the Wheels of Entrepreneurship? The
Impact of Regulations and Corruption on Firm Entry, June 2007 2014 Dominique Demougin and Claude Fluet, Rules of Proof, Courts, and Incentives, June
2007 2015 Stefan Lachenmaier and Horst Rottmann, Effects of Innovation on Employment: A
Dynamic Panel Analysis, June 2007 2016 Torsten Persson and Guido Tabellini, The Growth Effect of Democracy: Is it
Heterogenous and how can it be Estimated?, June 2007 2017 Lorenz Blume, Jens Müller, Stefan Voigt and Carsten Wolf, The Economic Effects of
Constitutions: Replicating – and Extending – Persson and Tabellini, June 2007 2018 Hartmut Egger and Gabriel Felbermayr, Endogenous Skill Formation and the Source
Country Effects of International Labor Market Integration, June 2007 2019 Bruno Frey, Overprotected Politicians, June 2007 2020 Jan Thomas Martini, Rainer Niemann and Dirk Simons, Transfer Pricing or Formula
Apportionment? Tax-Induced Distortions of Multinationals’ Investment and Production Decisions, June 2007
2021 Andreas Bühn, Alexander Karmann and Friedrich Schneider, Size and Development of
the Shadow Economy and of Do-it-yourself Activities in Germany, June 2007 2022 Michael Rauscher and Edward B. Barbier, Biodiversity and Geography, June 2007 2023 Gunther Schnabl, Exchange Rate Volatility and Growth in Emerging Europe and East
Asia, June 2007 2024 Erkki Koskela and Ronnie Schöb, Tax Progression under Collective Wage Bargaining
and Individual Effort Determination, June 2007
